Active learning of quantum system Hamiltonians yields query advantage
Hamiltonian learning is an important procedure in quantum system identification, calibration, and successful operation of quantum computers. Through queries to the quantum system, this procedure seeks to obtain the parameters of a given Hamiltonian model and description of noise sources. Standard te...
| Main Authors: | , , , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
American Physical Society
2023-07-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.5.033060 |
| _version_ | 1827285170614435840 |
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| author | Arkopal Dutt Edwin Pednault Chai Wah Wu Sarah Sheldon John Smolin Lev Bishop Isaac L. Chuang |
| author_facet | Arkopal Dutt Edwin Pednault Chai Wah Wu Sarah Sheldon John Smolin Lev Bishop Isaac L. Chuang |
| author_sort | Arkopal Dutt |
| collection | DOAJ |
| description | Hamiltonian learning is an important procedure in quantum system identification, calibration, and successful operation of quantum computers. Through queries to the quantum system, this procedure seeks to obtain the parameters of a given Hamiltonian model and description of noise sources. Standard techniques for Hamiltonian learning require careful design of queries and O(ε^{−2}) queries in achieving learning error ε due to the standard quantum limit. With the goal of efficiently and accurately estimating the Hamiltonian parameters within learning error ε through minimal queries, we introduce an active learner that is given an initial set of training examples and the ability to interactively query the quantum system to generate new training data. To ensure applicability on near-term quantum hardware, the active learner operates in batch mode as opposed to sequentially, proposing batches of queries to be made during learning. We formally specify and experimentally assess the performance of this Hamiltonian active learning (HAL) algorithm for learning the six parameters of a two-qubit cross-resonance Hamiltonian on four different superconducting IBM quantum devices. Compared with standard techniques for the same problem and a specified learning error, HAL achieves more than a 95% reduction in queries required, and upwards of 33% reduction over a sequential active learner. Moreover, with access to prior information on a subset of Hamiltonian parameters and given the ability to select queries with linearly (or exponentially) longer system interaction times during learning, HAL can exceed the standard quantum limit and achieve Heisenberg (or super-Heisenberg) limited convergence rates during learning. |
| first_indexed | 2024-04-24T10:10:35Z |
| format | Article |
| id | doaj.art-4eb82bb7d85f4596a0e98af5f2541965 |
| institution | Directory Open Access Journal |
| issn | 2643-1564 |
| language | English |
| last_indexed | 2024-04-24T10:10:35Z |
| publishDate | 2023-07-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj.art-4eb82bb7d85f4596a0e98af5f25419652024-04-12T17:32:50ZengAmerican Physical SocietyPhysical Review Research2643-15642023-07-015303306010.1103/PhysRevResearch.5.033060Active learning of quantum system Hamiltonians yields query advantageArkopal DuttEdwin PednaultChai Wah WuSarah SheldonJohn SmolinLev BishopIsaac L. ChuangHamiltonian learning is an important procedure in quantum system identification, calibration, and successful operation of quantum computers. Through queries to the quantum system, this procedure seeks to obtain the parameters of a given Hamiltonian model and description of noise sources. Standard techniques for Hamiltonian learning require careful design of queries and O(ε^{−2}) queries in achieving learning error ε due to the standard quantum limit. With the goal of efficiently and accurately estimating the Hamiltonian parameters within learning error ε through minimal queries, we introduce an active learner that is given an initial set of training examples and the ability to interactively query the quantum system to generate new training data. To ensure applicability on near-term quantum hardware, the active learner operates in batch mode as opposed to sequentially, proposing batches of queries to be made during learning. We formally specify and experimentally assess the performance of this Hamiltonian active learning (HAL) algorithm for learning the six parameters of a two-qubit cross-resonance Hamiltonian on four different superconducting IBM quantum devices. Compared with standard techniques for the same problem and a specified learning error, HAL achieves more than a 95% reduction in queries required, and upwards of 33% reduction over a sequential active learner. Moreover, with access to prior information on a subset of Hamiltonian parameters and given the ability to select queries with linearly (or exponentially) longer system interaction times during learning, HAL can exceed the standard quantum limit and achieve Heisenberg (or super-Heisenberg) limited convergence rates during learning.http://doi.org/10.1103/PhysRevResearch.5.033060 |
| spellingShingle | Arkopal Dutt Edwin Pednault Chai Wah Wu Sarah Sheldon John Smolin Lev Bishop Isaac L. Chuang Active learning of quantum system Hamiltonians yields query advantage Physical Review Research |
| title | Active learning of quantum system Hamiltonians yields query advantage |
| title_full | Active learning of quantum system Hamiltonians yields query advantage |
| title_fullStr | Active learning of quantum system Hamiltonians yields query advantage |
| title_full_unstemmed | Active learning of quantum system Hamiltonians yields query advantage |
| title_short | Active learning of quantum system Hamiltonians yields query advantage |
| title_sort | active learning of quantum system hamiltonians yields query advantage |
| url | http://doi.org/10.1103/PhysRevResearch.5.033060 |
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